th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China EFFECT OF NONLINEARITY IN PIER AND WELL FOUNDATION ON SEISMIC RESPONSE OF BRIDGES 1 2 Goutam Mondal and Sudhir K. Jain 1 PhD Scholar, Dept. of Civil Engineering, Indian Institute of Technology Kanpur, India 2 Professor, Dept. of Civil Engineering, Indian Institute of Technology Kanpur, India Email: [email protected], [email protected] ABSTRACT: Nonlinear seismic analysis of soil-well-pier system of a typical bridge supported on well foundation is carried out considering nonlinearity in piers and well. Bi-linear kinematic element is used to model nonlinearity in piers and well. Separation at the interface of soil and well is considered using compression-only gap elements. Analyses have been performed in two steps. In the first step, for a given acceleration time-history one- dimensional free-field analysis of the site is performed using SHAKE2000 to obtain the motion at the base of the soil profile. In the next step, this motion is applied at the base of finite element model of soil-well-pier system in SAP2000. The analysis has been carried out for different values of depth of scour and for two different earthquake motions in longitudinal direction. It is found that bending moment demand exceed the capacity by 20% to 70% in piers and 30% to 75% in well when piers and well are assumed to behave linearly. Subsequently, nonlinearity in piers is introduced when well is considered as linear. The analysis results show that nonlinearity in piers does not considerably reduce the force response of well. Therefore, nonlinearities in both piers and well are introduced in the next step. In this case, 15% to 50% reduction in rotational ductility demand in piers is observed but now the well must have adequate rotational ductility. KEYWORDS: Bridge, well foundation, caisson foundation, seismic analysis, nonlinear analysis 1. INTRODUCTION Well foundations are commonly used in the Indian subcontinent for both railway and road bridges on river streams. Seismic response of such foundations depends on several factors namely, shear modulus and hysteresis damping in soil, radiation damping, spatial variations of earthquake motion at different depths, nonlinearity at soil-well interface, nonlinearity in pier and well, hydrodynamic force, etc. Several researchers have analysed well foundation where the soil was modelled as lumped (Arya and Thakkar, 1970; Thakkar et al., 1991) or discrete springs (Arya and Thakkar, 1986). These approaches partially account for soil-well-pier interaction effects with nominal computational effort. More advanced methods account for soil-structure interaction (SSI) of well foundation; however, these methods do not account for nonlinearity in pier and well and/or at the interface of well and soil (Chang et al., 2000; Tsigginos et al., 2008; Zheng and Takeda, 1995). In the present study, nonlinear dynamic analysis of a typical bridge supported on well foundation is performed considering pier and well nonlinearity. Apart from that, interface nonlinearity and hydrodynamic effect are also considered. However, yielding of soil surrounding the well is not accounted for. The analysis has been performed for different values of depth of scour and for two different earthquake motions in longitudinal direction. 2. DESCRIPTION OF THE BRIDGE A typical bridge, simply supported on well foundations is considered for the present study (Figure 1). The substructure consists of two hollow circular reinforced concrete piers supported on a double-D hollow th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China reinforced concrete well foundation (Figure 1). The bridge decks are assumed to be simply supported on piers, and therefore, an isolated well and two piers are considered as a vibration unit during seismic analysis. Direction of Pier Earthquake Motion 11.35m 1 1 G.L. E.L. +30.0 5.3m Depth (m) (N1)60 ν Soil type 1.5 12 3.0 25 0.4 Silty Sand 3.3m 6.0 25 9.0 37 Well Section 1-1 12.0 36 15.0 55 0.3 Medium 16.5 56 Sand 19.5 57 2 2 22.5 57 25.5 58 18 m 28.5 58 E.L. +3.7 31.5 58 Seismic 34.5 58 51 m Scour 58 37.5 Gravel 0.2 11 m 40.5 58 Sand 43.5 58 Section 2-2 46.5 58 50.5 58 53.5 58 E.L. -21.0 55.17 58 Figure 1 Average soil profile along bridge alignment and schematic drawing of well foundation Figure 2 Acceleration time history for (a) SEE and (b) CME 3. ANALYSIS PROCEDURE The bridge is analysed for two different earthquake motions: Safety Evaluation Earthquake (SEE) and 1992 Cape Mendocino earthquake (CME) (Figure 2). SEE is specified with PGA of 0.6g caused by a magnitude 7.0 earthquake while CME is an independent near-field earthquake motion (epicentral distance 4.5 km) with PGA 0.662g. In this paper, these motions are applied in longitudinal direction only. Analysis has been performed in two steps (Figure 3). In the first step, one dimensional free-field analysis of the site is performed in SHAKE2000 using the above ground motions at the ground level of the soil column to obtain the motion at the base of the model. In this analysis strain-dependent shear modulus and damping are used to evaluate effective shear modulus and damping of soil at each layer. In the next step, these effective properties of soil are used to th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China perform nonlinear modal time history analysis of the soil-well-pier FE model in SAP2000 using the time history obtained from the previous step (Figure 3). Initially, both piers and well are assumed as linear. Later, pier nonlinearity in is introduced while well is assumed to behave as linear structure in order to examine the effect of pier nonlinearity on the response of well. If bending moment demand in well is more than the capacity, nonlinear analysis of the soil-well-pier model is performed considering nonlinearity in both piers and well. 4. FE MODELLING OF THE SYSTEM Figure 3 shows a schematic of idealisation of the entire structure. In the analysis, only mass of the superstructure is modelled and is applied at the pier cap. The mass of water in the enveloping cylinder of the submerged part of the well above the ground level is added to the structural mass. The mass of water and sand inside the well have been appropriately considered in the analysis. 2 3 Extension Pier ε 4 1 k 2 1 n Frame element Plane-strain area Massless rigid Compression Separation for well and pier element for soil Well outrigger element Gap element for (c) (d) soil-well interface Input time history Soil Gap element (e) Time history obtained Modal time history using SHAKE 2000 analysis in SAP 2000 (a) (b) Figure 3 Schematic representation of the analysis procedure and modelling of 2-D soil-well-pier model Piers and well are modeled as two-noded frame elements. Massless rigid-outrigger elements are added in the embedded part of the well to account for the breadth of the well when interacting with soil. Plastic hinges in piers are modelled by lumped plasticity model in the form of bi-linear kinematic rotational springs with degrading hysteretic loop recommended by Takeda et al. (1970). These springs are lumped at a distance Lp/2 from the bottom end of the piers where Lp is defined as (Priestley et al., 1996): Lp = 0.08l + 0.022 f y d b ≥ 0.044 f y db (4.1.1) where, l is the height of the piers (m), db is the diameter of longitudinal reinforcement (m), and fy is the yield strength of reinforcement (MPa). These springs are assumed to be rigid under shear and axial forces. Flexural deformation of the plastic hinge is taken care of by the spring elements and all the shear and axial deformations are taken by linear frame elements. Stiffness values of spring elements are defined by moment-rotation (M-θ) curves which are derived from the moment-curvature (M-φ) curves of the piers. M-φ curves have been derived from the moment–curvature analysis of piers and well section considering confinement model proposed by th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China Mander et al. (1988). Soil surrounding the well is modelled as four-noded two-dimensional plane-strain element (Figure 3). Element size in FE model is chosen such that it can satisfactorily represent propagating waves of desired frequency. However, as major part of the motion consists of vertically propagating waves with horizontal wave front, horizontal dimension of the elements can usually be chosen several times the vertical dimension (Lysmer et al., 1975). Here, the vertical dimension of the element is considered as 1.5 m while horizontal dimension gradually increases from 1.5 m at center to 5 m towards the boundary of the soil medium. Thickness of each soil element is taken as 18 m which is same as the well dimension perpendicular to the direction of motion. Vertical soil boundaries are restricted at 300 m away from the centre of well assuming that response of well will be unaffected by the boundary condition at the two vertical sides. Vertically fixed and horizontally free boundary conditions are applied at the two vertical boundaries of the model since this boundary condition converges faster to the infinitely long model (Agarwal, 2006). Bottom boundary is restricted at 35 m below the bottom of well and is restrained in both horizontal and vertical directions since it is considered that soil stratum is rested on hard rock.